Some math related code for calculatin binomial coef, nth-fibonacci and sin

fibmat.c

@@ -0,0 +1,62 @@
+#include <stdio.h>
+#include <stdint.h>
+
+/**
+ * @brief Computes the n-th Fibonacci number using matrix exponentiation.
+ *
+ * This implementation uses the identity:
+ *   [F(n+1) F(n)  ] = [1 1]^n
+ *   [F(n)   F(n-1)]   [1 0]
+ *
+ * The matrix is exponentiated in O(log n) time using exponentiation by squaring.
+ *
+ * @param n The index of the Fibonacci number to compute.
+ * @return The n-th Fibonacci number.
+ */
+uint64_t fibonacci_matrix(uint32_t n);
+
+// 2x2 matrix structure for Fibonacci computation
+typedef struct {
+    uint64_t a, b;
+    uint64_t c, d;
+} FibMatrix;
+
+/**
+ * @brief Multiplies two 2x2 matrices.
+ */
+static FibMatrix matrix_multiply(FibMatrix x, FibMatrix y) {
+    FibMatrix result;
+    result.a = x.a * y.a + x.b * y.c;
+    result.b = x.a * y.b + x.b * y.d;
+    result.c = x.c * y.a + x.d * y.c;
+    result.d = x.c * y.b + x.d * y.d;
+    return result;
+}
+
+/**
+ * @brief Raises a 2x2 matrix to the power of n using exponentiation by squaring.
+ */
+static FibMatrix matrix_power(FibMatrix base, uint32_t n) {
+    FibMatrix result = {1, 0, 0, 1}; // Identity matrix
+    while (n > 0) {
+        if (n % 2 == 1)
+            result = matrix_multiply(result, base);
+        base = matrix_multiply(base, base);
+        n /= 2;
+    }
+    return result;
+}
+
+uint64_t fibonacci_matrix(uint32_t n) {
+    if (n == 0) return 0;
+    FibMatrix base = {1, 1, 1, 0};
+    FibMatrix result = matrix_power(base, n - 1);
+    return result.a;
+}
+
+int main() {
+    for (uint32_t i = 0; i <= 20; ++i) {
+        printf("F(%u) = %lu\n", i, fibonacci_matrix(i));
+    }
+    return 0;
+}